Good Morning Shaun, 

Thank you for contacting the U of M Extension Service. 

If you have a 30 year old thriving river birch, you would not want to stress the tree by cutting the roots. 

You did not indicate how far the paver walkway is from the trunk of the tree. Is this one of the major tree roots, viewing the tree?   If the sidewalk is pavers, is it possible to move the pavers a few feet to accomodate the roots? 

If you chop one of the main roots of the tree to accomodate the sidewalk, it will probably cause stress to the tree making it more susceptible to diseases, pests and possibly cause it to die. 

Here is a link from the U of M Extension Yard and Garden website about river birch: 

https://extension.umn.edu/trees-and-shrubs/river-birch

You mght consider hiring a certified tree care professional to evaluate the situation and advise: 

https://extension.umn.edu/planting-and-growing-guides/how-hire-tree-care-professional

Good Luck!